Question

Part d dilate quadrilateral abcd again using the origin as the center of dilation with a scale factor of -0.5. find the area of the new quadrilateral, and calculate the ratio of the area of new quadrilateral to the area of the original quadrilateral.

Answer 1

To dilate a quadrilateral using the origin as the center of dilation with a scale factor of -0.5, multiply the coordinates of each vertex by the scale factor. Calculate the area of the new quadrilateral using the new coordinates.

Step-by-step explanation:

To dilate quadrilateral ABCD using the origin as the center of dilation with a scale factor of -0.5, we need to multiply the coordinates of each vertex of the quadrilateral by the scale factor. Let's say the original coordinates of the vertices are A(x1, y1), B(x2, y2), C(x3, y3), and D(x4, y4).

The new coordinates would be A'(x1*(-0.5), y1*(-0.5)), B'(x2*(-0.5), y2*(-0.5)), C'(x3*(-0.5), y3*(-0.5)), and D'(x4*(-0.5), y4*(-0.5)).

To find the area of the new quadrilateral, we can calculate the area of the quadrilateral using the original coordinates, and then use the same formula to calculate the area of the dilated quadrilateral using the new coordinates.